Hi, I'm using the following definition for the Fourier transform.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx}

[/tex]

(I used a capital F instead of f with a squiggle on top because the tex code doesn't seem to be working the way I intended it to.)

I have the function

[tex]

f\left( x \right) = \left\{ {\begin{array}{*{20}c}

{1,a < x < b} \\

{0,otherwise} \\

\end{array}} \right.

[/tex]

So [tex]F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx} [/tex]

[tex] = \int\limits_a^b {e^{iqx} dx} [/tex]

[tex]

= \frac{i}{q}\left( {e^{iqa} - e^{iqb} } \right)

[/tex]

According to the definition I'm using, is this the correct answer? I ask this because I'm not given an answer and I need to verify my answer by using the inverse Fourier transform. I haven't done complex analysis so integrals of ratios of exponentials and polynomials aren't things I can deal with right now. Which is why I'd like to know if I've taken the correct approach so that I can at least get through some questions.

Any help would be good thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fourier transform

**Physics Forums | Science Articles, Homework Help, Discussion**